Surface Multivariate Tensor-based Morphometry on ... - Yalin Wang

Surface Multivariate Tensor-based Morphometry on Premature Neonates: A Pilot Study Yalin Wang PhD1 , Ashok Panigrahy MD2,3 , Jie Shi1 , Rafael Ceschin2 , Marvin D. Nelson MD3 , Boris Gutman4 , Paul M. Thompson PhD4 , Natasha Lepor´e PhD3 1

School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ 85281, USA 2 Dept of Radiology, Children’s Hospital of Pittsburgh UPMC, Pittsburgh, PA, USA 3 Dept of Radiology, University of Southern California and Children’s Hospital, Los Angeles, CA 90027, USA 4 Lab of Neuro Imaging, UCLA School of Medicine, Los Angeles, CA 90095, USA

Abstract. Prematurity is one of the leading causes of mental retardation in the United States. Finding the neuroanatomical correlates of prematurity is vital to understanding which structures are affected, and in designing treatments. Using brain structural MRI, we perform regional group comparisons of the surface anatomy of subcortical structures between healthy preterm and term-born neonates. We first reconstruct the surfaces of subcortical structure from manually segmented brain MR images and we then build parametric meshes on the surfaces by computing surface conformal parameterization with holomorphic 1-forms. Surfaces are registered by constrained harmonic maps on the parametric domains and statistical comparisons between the two groups are performed via multivariate tensor-based morphometry (mTBM).We have processed a total of 5 subcortical structures, the corpus collosum, thalamus, caudate nucleus, hippocampus and putamen, as well as the lateral ventricle and the 3rd ventricle. In this pilot study, we apply mTBM to analyze the thalamus, lateral ventricle and hippocampus in 10 term-born and 10 preterm neonates. We detect statistically significant morphological changes in the majority of the right ventricle as well as in the left pulvinar, a result that validates earlier whole volume analyses in this structure. The hippocampus results, while not significant, show a trend that may be become significant with a larger data set. Our mTBM analysis is also compared to the more commonly used medial axis distance (MAD) [21, 6], and to the combination of both methods. MTBM gives more powerful results than MAD, and the combination of both further improves detection power.

1

Introduction

Babies born prematurely are more at risk of abnormal growth and mental development. Neurocognitive and neurosensory deficits in preterm neonates are likely related to abnormal development and injury of subcortical structures, including for example the corpus callosum, the thalamus, the basal ganglia and the hippocampus. With the advent of emerging new brain MR analysis techniques, it has become possible to detect and track how neurological disorders affects brain anatomy, and in particular the anatomy of subcortical structures. For example, hippocampal and

ventricular surface morphology have been increasingly studied in neurodevelopment and as markers of neurodegenerative disease research [1–7]. In neonates, subcortical structures from MRI images have been studied in several ways: The first is to manual segment the structure of interest for each subject in a data set and to compute its total volume. The volumes can then be statistically compared between a patient and a control group. This method may provide some preliminary insights into which structures may be affected; however, its detection and localization powers are both generally limited compared to more advanced vertexor voxel-based approaches, which provide maps of group differences over a structure or the whole brain. Hence, a few works have used voxel-wise morphometry instead (voxel-based morphometry (VBM) or tensor-based morphometry (TBM)), for which the whole brain volume is analyzed at once, and voxelwise differences are found between groups. In particular, for structural MRI data, [8] used TBM and found reduced thalamic and lentiform volumes in preterm infants, and a volume increase in the posterior horn of the ventricles. One VBM study used DTI data [9], and found increased fractional anisotropy (FA) in preterm infants. While these more generalized volumebased techniques have resulted in finding nonspecific global abnormalities in preterm neonates, they have not provided regional specificity in relation to the morphology of subcortical structures. Furthermore, most surface morphometric work in neonates has been dedicated solely to studying the cerebral cortex [10, 11]. Here we aim to zoom in on subcortical structures of interest, and to perform a surface-based analysis. Our aim is two-fold: First, using brain structural MRI, we propose a novel pipeline for group comparisons of the surface anatomy of subcortical structures in neonates. Fig. 1 illustrates our pipeline. To our knowledge, no one to date has attempted surface based statistics on subcortical structures in these subjects. As in studies of subcortical structures in adults (e.g. [12, 7]), we expect that our method will increase statistical power to detect statistical differences between the term born and premature groups, as well as improve localization of the changes. Secondly, we perform a group analysis using our pipeline on three structures that are thought to be affected by prematurity: the thalamus, the hippocampus and the lateral ventricles. Using brain T1- and T2- weighted MRI scans from 10 preterm and 10 term-born neonates, we aim to detect surface-based regional differences in shape between the two groups. In the current study, we focus exclusively on preterm neonates with no visible evidence of white matter injury as determined by an expert neuroradiologists, in order to demonstrate the power of our method to detect the subtle brain injuries that may be present in those subjects. Our method extends knowledge gained from the volume based analyses of neonates in the literature. Surface morphology in subcortical structures may be a useful indicator of brain injury. For example, shape differences in the hippocampus or the lateral ventricles are sensitive indicators of diffuse white matter injury and of the interrelated subcortical grey matter injury in adults [13–15], and we hypothesize that this is also the case in neonates. Based on results from studies (e.g. [16]), where the whole volume of the thalamus was analyzed, and on our preliminary work with a smaller data set [17], we expect to find morphometric differences in several subcortical structures in the preterm neonates compared to the term-born controls. In particular, [8] found differences in the pulvinar, a structure involved in cognitive visual processing. The methods described here are expected to have higher detection power compared to

whole volume based ones, and we expect that they will yield important results on the effect of prematurity on brain anatomy.

Fig. 1. Diagram of the proposed system. The subcortical structure image are segmented from T1 images. Surface mTBM is applied to analyze morphometric changes.

2 2.1

Method Surface Multivariate Tensor-based Morphometry (mTBM)

Our aim is to determine the intrinsic surface morphology of segmented subcortical structures in preterm neonates, by applying a multivariate tensor-based morphometry analysis (mTBM) [7]. In mTBM, given two data sets of segmented subcortical structures (for example, here MR images of the thalami from a group of preterm and one of term-born controls), each surface is represented by a conformal grid with indexed vertices, which give the correspondence between locations from different subjects images (see Fig. 2). Mathematically, holomorphic one-forms induce a special system of curves on a surface, the conformal grid. The computed conformal parameterization is one-to-one, angle-preserving and preserve small similarities between surfaces, so it is a powerful surface parameterization method [7]. We computed the holomorphic one-forms by solving a linear system so its computation is general and very stable [18]. Surfaces are registered to each other using a constrained harmonic map based on the conformal grid [18] to obtain corresponding locations between subjects for each subcortical structure. A statistical comparison between the two groups is performed at each corresponding vertex using the Jacobian of the transformation that put the images into correspondence [19, 7]. More precisely, for each subject in the data set, the registration yields a displacement field u between the template and the subject’s images. A Jacobian matrix J = Id + ∇u is computed at each vertex from the registration between template and subjects images, where Id is the identity matrix. In tensor-based morphometry, these Jacobian matrices, or a function of their components are typically used as

metrics for group comparisons. Several papers on comparisons of univariate (det J, trJ, ...) and multivariate (log S or their eigenvalues, where S are the deformation √ tensors S = JJ T ) measures were written by our groups and others to evaluate these different possible statistics for volume and surface TBM (see e.g. [19] for the volume-based mTBM and [7] for the surface-based one). In general, the multivariate measures yielded increased statistical power when compared to the univariate ones. As with studies on adults, we expect that the deformation tensors will outperform univariate measures in terms of detection power in neonates. To date, our surface mTBM method has been applied to study lateral ventricular morphology in HIV/AIDS [7], and has achieved the highest effect sizes when compared to univariate methods in a large ADNI morphometry study (N=804) of subcortical structures [12]. The current version of the software is publicly available at [20]. 2.2

Medial Axis Method (MAD)

One of the most commonly used morphometry measure on surface data is the radial distance ρ from a medial axis to a vertex of the surface [21, 6]. The medial axis is computed using the center point on the iso-parametric curves, i.e. the iso-parametric curve is perpendicular to the medial axis, on the computed conformal grid [22], after which ρ is easily found at each vertex. We will use MAD both as a validation and as a comparison tool for the statistical analysis in mTBM. We also use a combined MAD + mTBM statistic, for which a vector of all the different independent values we measured (all 3 independent components of the symmetric, positive definite log S and ρ) are treated as a multivariate measure which we use as a statistic for group comparisons. 2.3

Neonatal Data

Here we will use a dataset comprising 10 premature neonates (post-conception ages 25-36 weeks, 43.02 ± 1.7218 weeks at scan time) with normal MR scans and 10 healthy term born infants (post-conception ages 43.0150 ± 1.7392 weeks at scan time). T1 weighted MRI scans were acquired using a dedicated neonatal head coil on a 1.5T GE scanner using a coronal three-dimensional (3D) spoiled gradient echo (SPGR) sequence. We also used 3D T2 fast spin echo images on the same subjects. The inclusion criteria for our preterm subjects were the following: 1) prematurity (less than 37 gestational weeks at birth), and 2) visually normal scans on conventional MR imaging. All subjects with visible injuries were excluded from the dataset. The controls are neonates born at term (37 to 42 gestational weeks) with normal findings on conventional MR imaging performed in the same age range as the preterm cohort. The institutional review board at our medical center approved the study protocol. 2.4

Preprocessing

We manually segmented the corpus collosum, lateral ventricle, thalamus, hippocampus, caudate nucleus, putamen and the 3rd ventricle with Insight Toolkit’s SNAP program [23]. Tracings were done in the registered template space by an experienced pediatric neuroradiologist, using standard protocols. Fig. 2 shows the 7 reconstructed surfaces and their holomorphic one-forms for one subject.

Fig. 2. Reconstructed subcortical structure surfaces and their conformal grids, shown by texture mapping of checkboard images. The conformal structure is computed and used to register surface across subjects and compute the mTBM statistics.

2.5

Statistical Analysis

We run two permutation tests on the images, a vertex-based one that allows us not to assume a normal distribution, and one over the whole segmented image to correct for multiple comparisons [24, 19, 7]. In both cases, we randomly assign diagnostic labels (premature or term-born) to each subject, without replacement. A T 2 -test is performed at each vertex using the new labels, and p-values are found using the standard Hotelling’s T 2 -test for normally distributed data. The procedure is repeated 10000 times. For the first permutation test, we obtain a null distribution of T 2 -values at each vertex to which we compare the T 2 -values from the real data. For the second one, we compute a single value over the whole image for each of the 10000 permutations. The value we choose is Npi = number of p-values < 0.05 over all vertices in the image for permutation i. This provides us with a null distribution to which we compare Nptrue from the true labels.

3 3.1

Results Thalamus Results

Fig. 3 shows area of significant abnormality on the thalamus when comparing the preterm vs. the term group. All methods agree as to the location of clusters of significance, though the mTBM results are a bit noisier than those for MAD. However, the overall p-value for MAD is above the threshold for statistical significance - which we set here at pt = 0.05, given our a priori hypothesis on the thalamus -, while that for mTBM is much lower than pt .

Fig. 3. Thalamus statistical p-maps: Left columns: mTBM; middle columns: MAD; right columns: mTBM + MAD. Overall p-values on the left are p = 0.0101 for mTBM, p = 0.0566 for MAD and p = 0.0028 for MAD + mTBM.

The main cluster of significance is on the left pulvinar, a region that has previously been implicated in prematurity related thalamic injury (see e.g. [8]). In order to see the direction of the changes, we also mapped Np

k

R = log10

Σi

det Jpki

ΣjNc det Jckj

(1)

at each voxel k (see Fig. 6), where Jpki and Jcki are the Jacobian matrices for the preterm or term-born subject i, respectively, and Np and Nc are the numbers of preterm and term-born subjects. The determinant of the Jacobian matrix indicates the difference in size of the region in the individual subject compared to the template, with values greater than 1 indicating that the surface area at that vertex is larger in the subject when compared to the template, and vice-versa for values smaller than 1. As expected, the pulvinar is smaller on average in our preterm subjects compared to the controls. 3.2

Ventricle Results

Fig. 4. Ventricles statistical p-maps. Left columns: mTBM; middle columns: MAD; right columns: MAD + mTBM. Overall p-values are p = 0.0009 for mTBM, p = 0.0364 for MAD and p = 0.0003 for MAD + mTBM.

Fig. 4 shows the significant abnormality areas on the lateral ventricles between two groups. The right ventricles show widespread areas of significance with mTBM,

while the left ones do not. However, when looking at the determinant map Fig. 6, we see that the ventricles on both sides are smaller on average in the preterm compared to term-born groups, so the difference in results between the two sides may be due to our relatively small data set. While results are consistent for all 3 methods, the mTBM and combined statistics show a much larger area of significance, and lower overall p-values. 3.3

Hippocampus Results

Fig. 5. Hippocampus statistical p-maps. Left columns: mTBM; middle columns: MAD; right columns: MAD + mTBM. Overall p-values on the right are p = 0.1359 for mTBM and p = 0.3144 for MAD and p = 0.0577 for MAD + mTBM.

The hippocampus shows several clusters of significance, but fail to reach significance overall when corrected for multiple comparisons. However, a trend of p = 0.0577 is seen when combining mTBM and MAD, which may become significant as we increase the size of our dataset.

Fig. 6. Maps of the ratios of average determinants of the Jacobian matrices Rk , Eq. 1, for all 3 structures. From left to right: A. thalamus (ventral point-of-vue), B. ventricles, C. hippocampus. Area of regions that are statistically significant in Figs. 3, 4 and 5 are smaller on average in premature neonates compared to controls.

4

Discussion

We present the first surface subcortical structure morphometry study of neonatal brain MR images. We introduce a pipeline for the analysis of these images, and apply

it to compare a preterm and term-born group. Even in our relatively small data set, we detect significant differences between the premature and term-born groups. Hence, the methods described here are expected to have higher detection power compared to whole volume based ones, and we expect that they will yield important results on the effect of prematurity on brain anatomy. The preterm recruited in this study were admitted to a high risk NICU despite having normal conventional MRI, and may be at risk for diffuse white matter injury which could be missed by visual inspection of MRI. Since focal and diffuse white matter injury can result in white matter hypoplasia, there is likely a correlation with lateral ventricle changes and diffuse white matter injury. Diffuse white matter injury in the preterm may be also be associated with grey matter injury, as it is likely to disrupt cortical-thalamic fibers. This technique may be used to study the relationship between mild diffuse white matter injury, lateral ventricle size and associated grey matter injury. In the future, we plan on applying our method to larger data sets of premature neonates. We will also apply the method to a longitudinal study of the same patients, thus allowing us to correlate the baseline results with long-term cognitive outcome, which will potentially yield important predictors of learning deficits in premature children. These results may have implications for early prediction and long-term prognosis, which can be helped with implementing early specific behavior intervention for these preterm neonates, with the hope of reducing neurodevelopmental disabilities. Acknowledgments This work was partially funded through NIH grant 5K23NS063371.

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